1f:["$","div",null,{"className":"p-6 md:p-8","children":["$","h1",null,{"className":" prose prose-lg max-w-none break-words prose-headings:font-bold prose-headings:text-slate-900 prose-p:text-slate-700 prose-p:leading-relaxed prose-strong:text-slate-900 prose-ul:list-disc prose-ol:list-decimal prose-li:text-slate-700 mb-4 [&_table]:w-auto [&_table]:max-w-full [&_table]:border-collapse [&_th]:border [&_th]:border-slate-300 [&_th]:px-3 [&_th]:py-2 [&_th]:text-left [&_td]:border [&_td]:border-slate-200 [&_td]:px-3 [&_td]:py-2 [&_table]:my-4 overflow-x-auto","dangerouslySetInnerHTML":{"__html":"

Find the equation of the ellipse with foci at (±5,0) and x =36/5 as one of the directrices.

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We have ae = 5, a/e =36/5 which give a² = 36 or a = 6.

∴ e = 5/6

Now, b = a√(1 - e²) = 6√(1 -25/36) = √11

∴ The equation of the ellipse is x²/36 + y²/11 = 1.

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